Adding more fuel to rumors of a third-party White house bid, officials yesterday said Mayor Bloomberg will co-host a California forum on nonpartisan solutions to problems – with Gov. Arnold Schwarzenegger giving the keynote talk.

Bloomberg will jointly host the June 19 affair in Los Angeles with the city’s mayor, Antonio Villaraigosa, officials said.

The conference – dubbed “Ceasefire! Bridging the Political Divide” – pairs Bloomberg with Schwarzenegger, a GOPer who’s won applause for taking centrist positions on issues like the environment and who has called Bloomberg his “soulmate.”

And it’s the latest hint that, despite his public denials, Bloomberg could be positioning himself to run for the White House as a third-party candidate.

Bloomberg aides said they were invited by the Annenberg School for Communication at the University of Southern California, where the event will be held. Villaraigosa’s office didn’t immediately return calls.

Officials at the Annenberg School confirmed they had approached Bloomberg and Villaraigosa about the forum.

School spokesman Geoffrey Baum said the idea “sprang out of” a dinner hosted by Wallis Annenberg, daughter of the late philanthropist Walter Annenberg, last year, that honored both Bloomberg and Villaraigosa.

“It’s conceived of by the school,” Baum said, adding that both mayors and Schwarzenegger “embodied the types of things we’re focusing on in the conference.”

The forum will “shine a spotlight on where things are working more effectively right now” in state and local governments, rather than Washington, he said.

California-based GOP consultant Dan Schnur said it’s a fairly transparent move on Bloomberg’s part to raise his national profile.

“Whether he ends up running [for president] or not, Bloomberg’s obviously got a strong interest in raising the political center,” he said.

“So these types of events and conversations . . . give him a chance to encourage a center political movement.”